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The below work comprises the unsteady flow and enhanced thermal transportation for Carreau nanofluids across a stretching wedge. In addition, heat source, magnetic field, thermal radiation, activation energy, and convective boundary conditions are considered. Suitable similarity functions use to transmuted partial differential formulation into the ordinary differential form, which is solved numerically by the finite element method and coded in Matlab script. Parametric computations are made for faster stretch and slowly stretch to the surface of the wedge. The progressing value of parameter A (unsteadiness), material law index <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>, and wedge angle reduce the flow velocity. The temperature in the boundary layer region rises directly with exceeding values of thermophoresis parameter Nt, Hartman number, Brownian motion parameter Nb, <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>, Biot number Bi and radiation parameter Rd. The volume fraction of nanoparticles rises with activation energy parameter EE, but it receded against chemical reaction parameter <inline-formula><math display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula>, and Lewis number Le. The reliability and validity of the current numerical solution are ascertained by establishing convergence criteria and agreement with existing specific solutions.